Mathematisches Institut

Professoren

Prof. Dr. Zoltán Balogh

Member of Institute Management / Program Director MSc in Mathematics

Mathematisches Institut (MAI)

Telefon
+41 31 631 45 30
Fax
+41 31 631 85 10
E-Mail
zoltan.balogh@math.unibe.ch
Büro
221a
Postadresse
Universität Bern
Mathematisches Institut (MAI)
Sidlerstrasse 5
3012 Bern
Schweiz
Sprechstunde
jeweils am Donnerstag, 11.00 - 12.00 Uhr
Bitte vorher Termin per e-Mail vereinbaren!
Short Biography Education
  • Master's 1990 Babes-Bolyai University, Cluj, Romania
  • Ph.D. 1995, Michigan State University, USA
  • Habilitation 2000 University of Bern, Switzerland
Positions
  • 1990-1991 Assistant, Babes-Bolyai University, Cluj, Romania
  • 1991-1995 Assistant, Michigan State University, USA
  • 1995-2000 Postdoc, University of Bern, Switzerland
  • 2000-2001 Assistant Professor, University of Pittsburgh, USA
  • since 2001 Full Professor, University of Bern, Switzerland
Research Areas
  • Geometric analysis
  • Geometric measure theory
  • Quasi-conformal mappings
  • Carnot-Carathéodory spaces

Published papers

  •  Functional inequalities and Hamilton-Jacobi Equations in Geodesic Spaces. With Alexandre Engoulatov, Lars Hunziker, Outi Elina Maasalo. Potential Analysis, 36 (2012), 317--337. http://link.springer.com/article/10.1007%2Fs11118-011-9232-2     

  • Uniformly quasiregular maps on the compactified Heisenberg group. With Katrin Fässler, Kirsi Peltonen. Journal of Geometric Analysis, 22, (2012), 633-665. http://www.springerlink.com/content/85122744m457424h/

  • Modulus of Curve Families and Extremality of Spiral-Stretch Maps. With Katrin Fässler and Ioannis D. Platis.  Journal d'Analyse Mathématique, 113 (2011), 265--291. http://www.springerlink.com/content/f23n3330449440v3/

  • Exceptional Sets for Self-similar Fractals in Carnot Groups. With Reto Berger, Roberto Monti and Jeremy T. Tyson. Mathematical Proceedings of the Cambridge Philosophical Society (2010), 149: 147-172. http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7791501

  • Rectifiability and Lipschitz extensions into the Heisenberg group. With Katrin S. Fässler. Mathematische Zeitschrift, 263 (2009), no. 3, 673-683. http://www.springerlink.com/content/t47p054260626667/

  • Sub-Riemannian vs. Euclidean dimension
    comparison and fractal geometry on Carnot groups.
    With Jeremy T. Tyson, Ben Warhurst. Adv. Math. 220 (2009), no. 2, 560-619. http://www.sciencedirect.com/science/article/pii/S0001870808002740

  • Gromov's dimension comparison problem on Carnot groups. With Jeremy T. Tyson, Ben Warhurst. C. R. Math. Acad. Sci. Paris 346 (2008), no. 3-4, 135-138.

  •  Self-similar sets in doubling spaces. With Heiner Rohner. Illinois J. Math. 51 (2007), no. 4, 1275-1297

  • Absolute continuity of quasiconformal mappings on curves. With P. Koskela and S. Rogovin. Geom. Funct. Anal. 17 (2007), no. 3, 645-664

  • Lifts of Lipschitz maps and horizontal fractals in the Heisenberg group. With Regula Hoefer-Isenegger, Jeremy T. Tyson. Ergodic Theory Dynam. Systems 26 (2006), no. 3, 621 - 651.

  • Scaled-oscillation and regularity. With Marianna Csörnyei. Proc. Amer. Math. Soc. 134 (2006), no. 9, 2667 - 2675.

  • Sphericalization and flattening. With S. Buckley. Conform. Geom. Dyn. 9 (2005), 76 - 101 (electronic).

  • Hausdorff dimension of self-similar and self-affine fractals in the Heisenberg group. With J. Tyson. Proc. London Math. Soc. (3) 91 (2005), no. 1, 153 - 183.

  • The Stepanov differentiability theorem in metric measure spaces. With Kevin Rogovin and Thomas Zuercher. Journal of Geometric Analysis, 2004, 405 - 422.

  • Regularity of convex functions on Heisenberg groups. With M. Rickly. Ann. Scuola Norm. Sup. Pisa Cl. Sci (5), Vol. II (2003), 847 - 868.

  • Transversal R^d-actions on CR-manifolds and embeddability. With Ch. Leuenberger. Tohoku Math. J. (2) 55 (2003), no. 4, 507 - 527.

  • Accessible domains in the Heisenberg group. With R. Monti. Proc. Amer. Math. Soc. 132 (2004), no. 1, 97 - 106.

  • Fundamental solution for the Q-Laplacian and sharp Moser-Trudinger inequality in Carnot groups. With J. Manfredi and J. Tyson. J. Funct. Anal. 204 (2003), 35 - 49.

  • Size of characteristic sets and functions with prescribed gradients. J. für die Reine und Angewandte Mathematik 564 (2003), 63 - 83.

  • Geometric charaterizations of Gromov hyperbolicity. With S.M. Buckley. Inventiones Math. 153 (2003), 261 - 301.

  • Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric. With M. Rickly and F. Serra Cassano. Publicacions Math. 47 (2003), 237 - 259.

  • Potential theory in Carnot groups. With J. Tyson. Amer. Math. Soc. Contemp. Math. 320 (2003), 15 - 27.

  • Singular solutions, homogeneous norms and quasiconformal mappings in Carnot groups. With I. Holopainen and J. Tyson. Math. Ann. 324 (2002), no. 1, 159 - 186.

  • Polar coordinates on Carnot groups. With J. Tyson. Math. Z. 241 (2002), no. 4, 697 - 730.

  • Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group. J. Anal. Math. 83 (2001), 289 - 312.

  • Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains. With M. Bonk. Comment. Math. Helv. 75 (2000), no. 3, 504 - 533.

  • Lempert mappings and holomorphic motions in C^n. With K. Astala and H. M. Reimann. Géométrie complexe et systèmes dynamiques (Orsay, 1995). Astérisque No. 261 (2000), xi, 1 - 12.

  • Quasiconformality, quasisymmetry, and removability in Loewner spaces. With P. Koskela. With an appendix by Jussi Väisälä. Duke Math. J. 101 (2000), no. 3, 554 - 577.

  • Quasiconformal contactomorphisms and polynomial hulls with convex fibers. With Ch. Leuenberger. Canad. J. Math. 51 (1999), no. 5, 915 - 935.

  • Equivariant contactomorphisms of circular surfaces. Houston J. Math. 25 (1999), no. 2, 259 - 266.

  • Pseudoconvexity and Gromov hyperbolicity. With M. Bonk. C. R. Acad. Sci. Paris Sér. I, Math. 328 (1999), no. 7, 597 - 602.

  • Lengths of radii under conformal maps of the unit disc. With M. Bonk. Proc. Amer. Math. Soc. 127 (1999), no. 3, 801 - 804.

  • Higher-dimensional Riemann maps. With Ch. Leuenberger. Internat. J. Math. 9 (1998), no. 4, 421 - 442.

  • Conformally maximal polynomial-like dynamics and invariant harmonic measure. With I. Popovici and A. Volberg. Ergodic Theory Dynam. Systems 17 (1997), no. 1, 1 - 27.

  • Lempert mappings and symplectic forms. With Ch. Leuenberger. Proc. Amer. Math. Soc. 125 (1997), no. 11, 3289 - 3292.

  • Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications. With A. Volberg. Rev. Mat. Iberoamericana 12 (1996), no. 2, 299 - 336.

  • Geometric localization, uniformly John property and separated semihyperbolic dynamics. With A. Volberg. Ark. Mat. 34 (1996), no. 1, 21 - 49.

 

Current PhD Students

Completed PhD Theses

Dissertationen Prof. Dr. Zoltán Balogh
Katrin Fässler Extremal quasiconformal and uniformly quasiregular mappings on the Heisenberg group. 2011                                                                 
Reto Berger Size of tangencies to non-involutive distributions. 2011.   
Heiner Rohner Exceptional sets for self-similar fractals in Carnot groups. 2011.
Thomas Zürcher Hausdorff dimension and regularity of Sobolev functions. 2009.
Regula Hoefer-Isenegger Lipschitz Maps and Iterated Function Systems on Heisenberg Groups. 2007.
Matthieu Rickli On Questions of Existence and Regularity Related to Notions of Convexity in Carnot Groups. 2005.

Current PhD Students

Completed PhD Theses

Masterarbeiten Prof. Dr. Zoltán Balogh
Annina Iseli
Parematrizations of fractal curves. 2013.                                                               
Joseph Grossenbacher
Iterated Functions Systems and Fractals as their Invariant Sets. 2013   
Simon Aufdereggen
Theorems of Rademacher and Stepanov. 2012. 
Nadja Reber
Eigenschaften des Hardy–Littlewood-Maximaloperators. 2011.
Ingemar Imboden Dimension selbstaffiner Mengen im Rn. 2010.
Michel Chetelat
Jacobian determinants of diffeomorphisms. 2009.
Rahel Kaeser
Hausdorff dimension snd quasiconformal mappings on the Heisenberg group. 2009.
Michel Chetelat
Sards Theroem und Varianten. 2009.
Evelyn Brunner
How to measure the volume with a thread. 2009.
Karin Fässler
Extending Lipschitz Maps from Euclidean Spaces into Heisenberg Groups. 2007.
Lars Hunziker
The Hamilton-Jacobi Equation in Geodesic Spaces. 2007.
Reto Berger
Poincaré-Ungleichung und Lip-lip-Bedingung in metrischen Mass Räumen. 2005.
Heiner Rohner
Dimension Formulae and Open Set Condition for Self-Similar Fractals. 2004.
Thomas Zürcher
Differenzierbarkeit in metrischen Massräumen. 2004.
Matthieu Rickly
Invariant metrics and Hausdorff measures on Heisenberg groups. 2002.